The use of centrifugation for size classification (separating particulate matter into size fractions) is known in the art.
Separating powders into narrow particle-size ranges is accomplished through dispersion sedimentation. Sedimentation rate is given by Stokes' law of settling: ##EQU1## where v=a particle's settling velocity, h=the distance through which the particle settles, t=the time required for the particle to settle through distance h, r=the particle radius, g=acceleration due to gravity, .rho..sub.p =particle density, .rho..sub.m =density of the medium, .zeta.=liquid viscosity, and K=the particle-shape factor (2/9 for a sphere), which takes into account both a particle's volume and its cross-sectional area.
The sum of a medium's buoyant force and the drag on a submicrometer particle makes simple gravitational settling time-consuming and tedious, and therefore uneconomical. Increasing the settling forces through centrifugal sedimentation speeds settling. Because a particle's terminal velocity is proportional to the square of its size, large particles settle through a medium considerably faster than do smaller particles, allowing easy separation. For centrifugal separation, the Svedberg-Nichols modification of Stokes' law is applicable: ##EQU2## where t=the time required for a particle to settle through a distance x.sub.2 -x.sub.1, for x.sub.2 =the rotating radius of the centrifuge to the end point of the particle's travel path and x.sub.1 =the rotating radius of the centrifuge to the beginning point of the particle's travel path; .omega.=angular velocity of the centrifuge in radians/sec.; and r, .rho..sub.p, .rho..sub.m, .zeta., and K are as defined above.
Under traditional approaches, a specific particle-size classification ("cut") is achieved by first calculating the angular velocity and residence time required to force particles larger than the largest desired size out of the dispersion to form a sediment on the wall. The dispersion is placed in a centrifuge bowl and then centrifuged under these calculated conditions, and the resulting overflow, containing only particles finer than the upper limit of the desired increment, is decanted. The overflow is then processed in a fashion similar to that used for the original dispersion, so that all particles larger than the lowest size desired are spun out of suspension onto the centrifuge wall. This second sediment consists of particles within the desired size range and is therefore retained.